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MechanicsBeam Deflection Calculator - Cantilever Beam
Deflection (δ) = (3 × F × L³) / (E × I)
Where:
- F = Force applied at the free end (e.g., the weight of the balcony and occupants)
- L = Length of the beam
- E = Modulus of Elasticity of the beam material
- I = Moment of Inertia of the beam's cross-section
Example-1 : Practical Use of Beam Deflection Calculator: Balcony Cantilever Beam
Diagram of the cantilever beam with force applied at the free end.
Imagine you're designing a balcony supported by a cantilever beam. The beam is fixed at one end (attached to the building) and free at the other. You need to ensure that the deflection of the beam is within safe limits to prevent structural issues and ensure the safety of the occupants.
Calculation:
Let's calculate the deflection at the free end of the beam using the formula:
Deflection (δ) = (3 × F × L³) / (E × I)
Where:
- F = Force applied at the free end (e.g., the weight of the balcony and occupants)
- L = Length of the beam
- E = Modulus of Elasticity of the beam material
- I = Moment of Inertia of the beam's cross-section
Example Values:
- F = 5000 N (500 kg balcony weight)
- L = 3 meters
- E = 200 GPa (Steel)
- I = 8 × 10⁻⁶ m⁴ (Rectangular cross-section)
Using these values in the formula:
δ = (3 × 5000 × 3³) / (200 × 10⁹ × 8 × 10⁻⁶) = 0.014 m (14 mm)
So, the deflection at the free end of the beam is 14 mm, which should be checked against allowable deflection limits for safety.
